# The Anscombe Quartet (R)

# demonstration data from
# Anscombe, F. J. 1973, February. Graphs in statistical analysis. 
#  The American Statistician 27: 17–21.

# define the anscombe data frame
anscombe <- data.frame(
    x1 = c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5),
    x2 = c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5),
    x3 = c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5),
    x4 = c(8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8),
    y1 = c(8.04, 6.95,  7.58, 8.81, 8.33, 9.96, 7.24, 4.26,10.84, 4.82, 5.68),
    y2 = c(9.14, 8.14,  8.74, 8.77, 9.26, 8.1, 6.13, 3.1,  9.13, 7.26, 4.74),
    y3 = c(7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73),
    y4 = c(6.58, 5.76,  7.71, 8.84, 8.47, 7.04, 5.25, 12.5, 5.56, 7.91, 6.89))

# show results from four regression analyses
with(anscombe, print(summary(lm(y1 ~ x1, data = anscombe))))
with(anscombe, print(summary(lm(y2 ~ x2, data = anscombe))))
with(anscombe, print(summary(lm(y3 ~ x3, data = anscombe))))
with(anscombe, print(summary(lm(y4 ~ x4, data = anscombe))))

# place four plots on one page using standard R graphics
# ensuring that all have the same scales
# for horizontal and vertical axes
pdf(file = "fig_anscombe_R.pdf", width = 8.5, height = 8.5)
par(mfrow=c(2,2), mar=c(5.1, 4.1, 4.1, 2.1))
with(anscombe, plot(x1, y1, xlim=c(2,20), ylim=c(2,14), pch = 19, 
    col = "darkblue", cex = 1.5, las = 1, xlab = "x1", ylab = "y1"))  
title("Set I")
with(anscombe,plot(x2, y2, xlim=c(2,20), ylim=c(2,14), pch = 19, 
    col = "darkblue", cex = 1.5, las = 1, xlab = "x2", ylab = "y2"))
title("Set II")
with(anscombe,plot(x3, y3, xlim=c(2,20), ylim=c(2,14), pch = 19, 
    col = "darkblue", cex = 1.5, las = 1, xlab = "x3", ylab = "y3"))
title("Set III")
with(anscombe,plot(x4, y4, xlim=c(2,20), ylim=c(2,14), pch = 19, 
    col = "darkblue", cex = 1.5, las = 1, xlab = "x4", ylab = "y4"))
title("Set IV")
dev.off()

# par(mfrow=c(1,1),mar=c(5.1, 4.1, 4.1, 2.1))  # return to plotting defaults

# Suggestions for the student:
# See if you can develop a quartet of your own, 
# or perhaps just a duet, two very different data sets 
# with the same fitted model.
